The Effect of the Metal Oxidation on the Vacuum Chamber Impedance
|
|
- Abel Bridges
- 5 years ago
- Views:
Transcription
1 SL-FL 9-5 The ffec of he Meal Oiaion on he Vacuum Chambe Impeance nani Tsaanian ambug Univesiy Main Dohlus, Igo agoonov Deusches leconen-sinchoon(dsy bsac The oiaion of he meallic vacuum chambe inenal suface is an accompanying pocess of he chambe fabicaion an suface eamen. This cicumsance changes he eleco ynamical popeies of he wall maeial an as consequence he impeance of he vacuum chambe. In his pape he esuls of longiuinal impeance fo oiise meallic vacuum chambe is pesene. The suface impeance maching echnique is use o calculae he vacuum chambe impeances. The loss faco is given fo vaious oies an oiaion hicness. The numeical esuls fo he unulao vacuum chambe of uopean XFL poec ae pesene. Inoucion The nowlege of he vacuum chambe impeance in acceleaos is an impoan issue o povie he sable opeaion of he faciliy fom he machine pefomance an beam physics poin of view []. The impeances of meallic ype vacuum chambes have been suie, fo eample, in [-], incluing he analyical pesenaion of he longiuinal an ansvese impeances fo laminae walls of iffeen maeials [8-] an finie elaivisic faco of he paicle [,]. The meal-ielecic vacuum chambe impeances have been suie in ef [-4]. In [4] he longiuinal an ansvese impeances fo he uopean XFL [5] ice vacuum chambe ae calculae base on he fiel ansfomaion mai echnique []. geneal appoach o evaluae he impeances of he muliplaye vacuum chambe is he fiel maching echnique. In his pape, he longiuinal impeance of meallic vacuum chambe wih inenal suface oiaion is suie fo ulaelaivisic beam case. The eplici analyical soluion is obaine fo vaious hicnesses of he meallic laye an oiaion eph. Base on he obaine esuls he impeance of uopean XFL unulao aluminium vacuum chambe is calculae fo vaious oiaion ephs. The eplici analyical soluion fo longiuinal impeance of wo-laye ube is obaine. The eac fomula fo ula elaivisic poin lie chage moving on ais is inouce in ems of suface impeance. I is shown ha in small oie eph asympoic limi he suface impeance on bounay wih vacuum can be esimae as a sum of oie an meal suface impeances. Base on his soluion he monopole impeances fo aluminium beam pipe wih iffeen oie laye hicness ae evaluae.
2 . eflecion of elecomagneic fiels on bounay of wo maeials Plane waves of any polaiaion can be escibe as a supeposiion of waves wih pepenicula (-moe an paallel (-moe polaiaions o he plane of incien [6, 7]. Le us invesigae he eflecion of hese waves wih pepenicula an paallel polaiaions (fig. fo he case when maeial has finie hicness. The case wih infinie wall hicness can be foun as a limi. Fo monopole beam impeance, which will be iscusse in ne he chape, only -moe is elevan. So in his chape we will mainly focus on -moe. -Moe y -Moe y -Moe y -Moe -Moe y -Moe y -Moe y Fig. eflecion of plane waves wih pepenicula (lef an paallel (igh polaiaions fom maeial suface which has finie hicness. The -componen of magneic fiel fo -moe an he same componen of elecical fiel fo -moe ae ( ( ( ( ef in ef in (, (, ep ep ep ep + wih cos sin, m ef in Whee he uppe ine escibe he maeial numbe, own ine escibe he polaiaion an poecion of fiel. Fom Mawell s equaion we ge he ansvese componen of elecic an magneic fiels fo boh ins of polaiaions coesponenly SL-FL 9-5
3 SL-FL 9-5 (, (, y (, y (, cos cos in ef ( ep( + ep( in ef ( ep( ep( By using he view of fiel componens we can easily fin he suface impeance ( ( (, (, (, (, (, (, (, y cos + (, y (, y + (, y cos Whee an ae he eflecion coefficiens. Taing o accoun he wave veco view fo suface impeance we ge + ( ±,, (, [cos] (, The eface wave fiel componens fo moe ae (, (, a y, in ef ep( b ep( in ef [ a ep( + b ep( ] wih in, ef, m, y n fo moe (, (, a y, in ef ( b ep( in ef [ a ep( + b ep( ] ep Fo suface impeance we ge ( (a, (, y y, (, ( (, y + (a (,, (, (, (, y (, y + y, whee, b, / a, ( whee he uppe ine (a shows he fis bounay of secon maeial.
4 SL-FL 9-5 Taing ino accoun he bounay coniions which leas o have coninuous angenial componen of wave veco,,, sin Using ne elaion of wave vecos beween wo meias ( We can easily fin ne esul (a (a (, (, sin + sin + α + α + Whee α sin Fo he secon bounay he suface impeance eas ( y, (b,, (, y ±, e, (, α ( (4 y,,, (, y +, e Fo hi maeial he fiel componens fo moe ae (, g (, n fo moe we have (, (, g g ep ep ( (, y g ( ep( y, y, ep ( n fo suface impeance we ge ne esul coesponenly whee,, y 4
5 SL-FL 9-5 ( ( (, (, (, (, (, (, (, y y, (, y (, y (, y y, sin sin whee is hicness of maeial. Using ne noaion an equaion ( we ge α sin (5 ( ±, (, α In he case when,, >> he α, appoimaion is vali. Now by maching ( (b he impeances (, wih (, coesponenly,, we fin he unnown coefficiens an,, y, m ( e whee, α (, (6 +, (a ( By maching (, wih (, we fin he eflecion coefficiens fo boh, polaie fiels inepenenly,, u, (, wih u +, u u ( ( / cos a (, a (, cos / ( In he case when he hi maeial is pefec conuco (, fo suface impeance fomula is simplifie (a (a y, (, anh( (, anh( y, y, y, y, an( y, an( y, y, (7 Whee he y-componen of wave veco in secon maeial has he ne view 5
6 SL-FL 9-5 y, sin In hin oie eph (<< limi suface impeances will eas (a (a (, (, sin Fo non-magneic maeials his fomula is simplifie (a (a (, (,, sin, Whee is elaive ielecic pemeabiliy. Fo incien angle π / we ge (a (a (, π / (, π /,, Le ewie his equaions in ne fom (a (a (, ( L L ( L L, sin, (8 Since he unis of paamees L, ae he same as fo inucance, he hin ielecic coaing impac on beam impeance can be consiee as influence of inuco impeance. In he case when he hi maeial is no pefec conuco in mos pacical cases he >> is fulfille an he suface impeance fo boh in of moes ae equal an eas as ( ( ( ( ( ( κ( κ Whee κ( is conuciviy of conuco wih τ - elaaion ime. + τ 6
7 SL-FL 9-5 Taing ino accoun noaion in eq.(6 afe some manipulaions fo suface impeance on bounay beween vacuum an fis maeial we ge (a (a y, (, (, y, an( an( y, y, y, an + + y, ( y, + an( y, an ( y, an( y, (9 The coefficiens, we igh in ne fom y, y, ( ( ( ( Fo hin ielecic (<< he asympoic fomula will eas (a (,, sin, ( ( ( (a ( (, + sin + Finally aing ino accoun noaions in eq.(7 an smallness of ielecic laye hicness we ge (a L κ, (, ( ( + +, (, + ( ( Whee meaning of he inees L an κ ae inuco an conuco coesponenly.. Beam Impeance Consie he elaivisic poin chage Q moving wih spee of ligh along he ais of unifom, cicula-cylinical wo-laye ube of inne aius (Fig.. The chage isibuion is hen given by Q(,, Qδ ( δ ( δ ( v. The secon laye has infinie hicness while he hicness of fis one is. The coss secion of he ube is ivie ino hee concenic egions: (vacuum, + (fis laye, + < (secon laye. 7
8 SL-FL 9-5 I b φ Fig. Geomey of he poblem In geneal, when he chage has non-eo offse, ue o cuen aial asymmey he fiels aiae in he ube have all si componens,,,, an, while in paicula case when i is on ais only hee componens ae ecie,, an hey ae inepenen on aimuhal cooinae ef [4]. The Mawell s equaions in fequency ( c omain (, ~ e fo moe will eas (. ( J (. (. Whee c 77Ω is he impeance of fee space. c Fom equaion (. an (. follows ha he longiuinal componen of elecic fiel is consan cons ( Subsiuing o he secon equaion we ge ( Le us ewie above equaion in ne fom J + 8
9 9 ( J + ( Taing ino accoun he elaion beween cuen an cuen ensiy J S J I S The inegaion of equaion ( gives π π I + n fo aimuhal componen of magneic fiel we ge I + π Finally all componens of M fiel will ea + + c c c e e I e I π π (4 The beam impeance will be b I The unnown coefficien shoul be foun fom bounay coniion. s The suface impeance on fis bounay coul be foun using maching echnique. In ems of suface impeance fo his coefficien i is easy o ge following epession SL-FL 9-5
10 SL-FL 9-5 s I π + Finally fo beam impeance we ge c s b s π + c s Whee suface impeance can be foun using he fomulas eive in pevious chape whee shoul be aen ino accoun ha he elecomagneic fiel ecie by ulaelaivisic chage has only ansvese componens which leas of π / incien angle. L s ( L L L κ s( s ( + s ( whee κ wih s ( κ κ( κ( + τ This fomula coincies wih hin coaing asympoic limi of eac soluion fo beam impeance of wo laye ube eive in ef [,].. Numeical esuls In his secion we pesen esuls of influence of hin oie laye on loss faco an enegy spea. Wae poenial of a Gaussian bunch wih σ 5 m ms lengh was calculae b 7 5 fo aluminium ( κ.7 Ω, τ 7. s beam pipe wih 5mm aius. To evaluae loss faco an enegy spea ne fomulas have been use Loss faco < W > negy spea W(s λ(s s < (W < W > > (W(s < W > λ(s s Whee W (s is a wae poenial an isibuion funcion. λ s ( s ep σ is a nomalie Gaussian πσ b b
11 SL-FL 9-5 a Loss faco [ V/pC/m ] 5 b Oie hicness [ nm ] negy spea [V/pC/m] 5 Oie hicness [nm] Fig. Loss faco an enegy spea vesus oie hicness fo iffeen in of oies. In figue ae ploe loss faco an enegy spea vesus oie laye hicness. The calculaions ae one fo hee ype of oies wih elaive ielecic pemiiviy, 5 an.
12 SL-FL 9-5 a 5 nm Loss faco [ V/pC/m ] 4 nm nm nm nm b Oie 5 nm negy spea [V/pC/m] 4 nm nm nm nm Oie Fig 4. Loss faco an enegy spea vesus oie ielecic pemiiviy fo iffeen hicness. In figue 4 ae ploe loss faco an enegy spea vesus oie elaive ielecic pemiiviy. s we see fom boh figues (, 4 he influence of oie laye in a wos case when aleay a 5 nm hicness inceases he loss facos moe han 6%. Since i is unnown he popeies an hicness of oie laye which is appeaing uing manufacuing of acceleao pas in ne figue we mae invesigaion fo he wos oie. In figue 5 is ploe he loss facos vesus oie hicness fo iffeen beam pipe aiuses.
13 SL-FL 9-5 a mm Loss faco [ V/pC/m ] 4mm 6mm 8mm mm Oie hicness [ nm ] b mm negy spea [V/pC/m] 4mm 6mm 8mm mm Oie hicness [nm] Fig 5. Loss faco an enegy spea vesus oie hicness fo iffeen beam pipe aiuses. In uopean XFL poec he unulao secions ae esigne wih aluminium vacuum chambes wih ellipical coss secions. The ellipse iamees in boh planes ae 5mm an 8.8mm coesponenly. Losses in ha secion can be esimae by oun beam pipe moel wih aius 4.4mm. s we can see fom figue 5 aleay a 6nm oie hicness he losses inceases wo imes wih espec o ieal case (no oie.
14 SL-FL 9-5 efeences. B.W.oe an S..Kheife, Impeances an Waes in igh-negy Paicle cceleaos (Wol Scienific, Singapoe, ene an O. Napoly, in Poceeings of he Secon uopean Paicle cceleao Confeence, Nice, Fance, 99 (iions Fonies, Gif-su-Yvee, 99, pp Piwinsi, I Tans. Nucl. Sci. 4, 64 ( Piwinsi, epo No. DSY-94-68, 994, p.. 5..W. Chao, Technical epo No. 946, SLC-PUB, 98; see also.w. Chao, Physics of Collecive Beam Insabiliies in igh negy cceleaos (Wiley, New Yo, B. oe, Pa. ccel., ( D. Jacson, SSCL epo No. SSC-N-, M. Ivanyan an V. Tsaanov, Phys. ev. ST ccel. Beams 7, 44 (4. 9..M. l-haeeb,.w. asse, O. Boine-Fanenheim, W.M. Daga an I. ofmann, Phys. ev. ST ccel. Beams,, 644 (7.. M. Ivanyan an V. Tsaanian, Phys. ev. ST ccel. Beams, 9, 444 (6.. N. Wang an Q. Qin, Phys. ev. ST ccel. Beams,, (7.. M. Ivanyan e al, Phys.ev.ST ccel.beams, 84 (8... Buov an. Novohasii, INP-Novosibis, epo No. 9-8, Tsaanian, M. Ivanyan, J. ossbach, PC8-TUPP76, Jun 4, M.laelli,.Binmann e al (eios, XFL. The uopean X-ay Fee- lecon Lase, DSY 6-97, July Collin, Founaion fo Micowave ngineeing, McGaw-ill, M. Bon,. Wolf, Pinciples of Opics,(986 4
ENGI 4430 Advanced Calculus for Engineering Faculty of Engineering and Applied Science Problem Set 9 Solutions [Theorems of Gauss and Stokes]
ENGI 44 Avance alculus fo Engineeing Faculy of Engineeing an Applie cience Poblem e 9 oluions [Theoems of Gauss an okes]. A fla aea A is boune by he iangle whose veices ae he poins P(,, ), Q(,, ) an R(,,
More informationLecture 22 Electromagnetic Waves
Lecue Elecomagneic Waves Pogam: 1. Enegy caied by he wave (Poyning veco).. Maxwell s equaions and Bounday condiions a inefaces. 3. Maeials boundaies: eflecion and efacion. Snell s Law. Quesions you should
More informationLecture 5. Chapter 3. Electromagnetic Theory, Photons, and Light
Lecue 5 Chape 3 lecomagneic Theo, Phoons, and Ligh Gauss s Gauss s Faada s Ampèe- Mawell s + Loen foce: S C ds ds S C F dl dl q Mawell equaions d d qv A q A J ds ds In mae fields ae defined hough ineacion
More informationTwo-dimensional Effects on the CSR Interaction Forces for an Energy-Chirped Bunch. Rui Li, J. Bisognano, R. Legg, and R. Bosch
Two-dimensional Effecs on he CS Ineacion Foces fo an Enegy-Chiped Bunch ui Li, J. Bisognano,. Legg, and. Bosch Ouline 1. Inoducion 2. Pevious 1D and 2D esuls fo Effecive CS Foce 3. Bunch Disibuion Vaiaion
More informationThe Production of Polarization
Physics 36: Waves Lecue 13 3/31/211 The Poducion of Polaizaion Today we will alk abou he poducion of polaized ligh. We aleady inoduced he concep of he polaizaion of ligh, a ansvese EM wave. To biefly eview
More informationControl Volume Derivation
School of eospace Engineeing Conol Volume -1 Copyigh 1 by Jey M. Seizman. ll ighs esee. Conol Volume Deiaion How o cone ou elaionships fo a close sysem (conol mass) o an open sysem (conol olume) Fo mass
More informationChapter 7. Interference
Chape 7 Inefeence Pa I Geneal Consideaions Pinciple of Supeposiion Pinciple of Supeposiion When wo o moe opical waves mee in he same locaion, hey follow supeposiion pinciple Mos opical sensos deec opical
More informationSharif University of Technology - CEDRA By: Professor Ali Meghdari
Shaif Univesiy of echnology - CEDRA By: Pofesso Ali Meghai Pupose: o exen he Enegy appoach in eiving euaions of oion i.e. Lagange s Meho fo Mechanical Syses. opics: Genealize Cooinaes Lagangian Euaion
More information, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t
Lecue 6: Fiis Tansmission Equaion and Rada Range Equaion (Fiis equaion. Maximum ange of a wieless link. Rada coss secion. Rada equaion. Maximum ange of a ada. 1. Fiis ansmission equaion Fiis ansmission
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES In igid body kinemaics, we use he elaionships govening he displacemen, velociy and acceleaion, bu mus also accoun fo he oaional moion of he body. Descipion of he moion of igid
More information( ) exp i ω b ( ) [ III-1 ] exp( i ω ab. exp( i ω ba
THE INTEACTION OF ADIATION AND MATTE: SEMICLASSICAL THEOY PAGE 26 III. EVIEW OF BASIC QUANTUM MECHANICS : TWO -LEVEL QUANTUM SYSTEMS : The lieaue of quanum opics and lase specoscop abounds wih discussions
More informationProjection of geometric models
ojecion of geomeic moels Copigh@, YZU Opimal Design Laboao. All ighs eseve. Las upae: Yeh-Liang Hsu (-9-). Noe: his is he couse maeial fo ME55 Geomeic moeling an compue gaphics, Yuan Ze Univesi. a of his
More informationLecture 18: Kinetics of Phase Growth in a Two-component System: general kinetics analysis based on the dilute-solution approximation
Lecue 8: Kineics of Phase Gowh in a Two-componen Sysem: geneal kineics analysis based on he dilue-soluion appoximaion Today s opics: In he las Lecues, we leaned hee diffeen ways o descibe he diffusion
More informationSPHERICAL WINDS SPHERICAL ACCRETION
SPHERICAL WINDS SPHERICAL ACCRETION Spheical wins. Many sas ae known o loose mass. The sola win caies away abou 10 14 M y 1 of vey ho plasma. This ae is insignifican. In fac, sola aiaion caies away 4 10
More informationÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s
MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN
More informationMATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH
Fundamenal Jounal of Mahemaical Phsics Vol 3 Issue 013 Pages 55-6 Published online a hp://wwwfdincom/ MATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH Univesias
More informationLecture-V Stochastic Processes and the Basic Term-Structure Equation 1 Stochastic Processes Any variable whose value changes over time in an uncertain
Lecue-V Sochasic Pocesses and he Basic Tem-Sucue Equaion 1 Sochasic Pocesses Any vaiable whose value changes ove ime in an unceain way is called a Sochasic Pocess. Sochasic Pocesses can be classied as
More informationToday - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations
Today - Lecue 13 Today s lecue coninue wih oaions, oque, Noe ha chapes 11, 1, 13 all inole oaions slide 1 eiew Roaions Chapes 11 & 1 Viewed fom aboe (+z) Roaional, o angula elociy, gies angenial elociy
More informationExponential and Logarithmic Equations and Properties of Logarithms. Properties. Properties. log. Exponential. Logarithmic.
Eponenial and Logaihmic Equaions and Popeies of Logaihms Popeies Eponenial a a s = a +s a /a s = a -s (a ) s = a s a b = (ab) Logaihmic log s = log + logs log/s = log - logs log s = s log log a b = loga
More informationLecture 17: Kinetics of Phase Growth in a Two-component System:
Lecue 17: Kineics of Phase Gowh in a Two-componen Sysem: descipion of diffusion flux acoss he α/ ineface Today s opics Majo asks of oday s Lecue: how o deive he diffusion flux of aoms. Once an incipien
More informationSTUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE WEIBULL DISTRIBUTION
Inenaional Jounal of Science, Technology & Managemen Volume No 04, Special Issue No. 0, Mach 205 ISSN (online): 2394-537 STUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE
More informationProjection of geometric models
ojecion of geomeic moels Eie: Yeh-Liang Hsu (998-9-2); ecommene: Yeh-Liang Hsu (2-9-26); las upae: Yeh-Liang Hsu (29--3). Noe: This is he couse maeial fo ME55 Geomeic moeling an compue gaphics, Yuan Ze
More informationOrthotropic Materials
Kapiel 2 Ohoopic Maeials 2. Elasic Sain maix Elasic sains ae elaed o sesses by Hooke's law, as saed below. The sesssain elaionship is in each maeial poin fomulaed in he local caesian coodinae sysem. ε
More informationFig. 1S. The antenna construction: (a) main geometrical parameters, (b) the wire support pillar and (c) the console link between wire and coaxial
a b c Fig. S. The anenna consucion: (a) ain geoeical paaees, (b) he wie suppo pilla and (c) he console link beween wie and coaial pobe. Fig. S. The anenna coss-secion in he y-z plane. Accoding o [], he
More informationIMPROVED DESIGN EQUATIONS FOR ASYMMETRIC COPLANAR STRIP FOLDED DIPOLES ON A DIELECTRIC SLAB
IMPROVED DESIGN EQUATIONS FOR ASYMMETRIC COPLANAR STRIP FOLDED DIPOLES ON A DIELECTRIC SLAB H.J. Visse* * Hols Cene TNO P.O. Bo 855 565 N Eindhoven, The Nehelands E-mail: hui.j.visse@no.nl eywods: Coupled
More informationTime-Space Model of Business Fluctuations
Time-Sace Moel of Business Flucuaions Aleei Kouglov*, Mahemaical Cene 9 Cown Hill Place, Suie 3, Eobicoke, Onaio M8Y 4C5, Canaa Email: Aleei.Kouglov@SiconVieo.com * This aicle eesens he esonal view of
More informationPH126 Exam I Solutions
PH6 Exam I Solutions q Q Q q. Fou positively chage boies, two with chage Q an two with chage q, ae connecte by fou unstetchable stings of equal length. In the absence of extenal foces they assume the equilibium
More informationr r r r r EE334 Electromagnetic Theory I Todd Kaiser
334 lecoagneic Theoy I Todd Kaise Maxwell s quaions: Maxwell s equaions wee developed on expeienal evidence and have been found o goven all classical elecoagneic phenoena. They can be wien in diffeenial
More informationMonochromatic Wave over One and Two Bars
Applied Mahemaical Sciences, Vol. 8, 204, no. 6, 307-3025 HIKARI Ld, www.m-hikai.com hp://dx.doi.og/0.2988/ams.204.44245 Monochomaic Wave ove One and Two Bas L.H. Wiyano Faculy of Mahemaics and Naual Sciences,
More informationEnergy dispersion relation for negative refraction (NR) materials
Enegy dispesion elaion fo negaive efacion (NR) maeials Y.Ben-Ayeh Physics Depamen, Technion Isael of Technology, Haifa 3, Isael E-mail addess: ph65yb@physics.echnion,ac.il; Fax:97 4 895755 Keywods: Negaive-efacion,
More information7 Wave Equation in Higher Dimensions
7 Wave Equaion in Highe Dimensions We now conside he iniial-value poblem fo he wave equaion in n dimensions, u c u x R n u(x, φ(x u (x, ψ(x whee u n i u x i x i. (7. 7. Mehod of Spheical Means Ref: Evans,
More informationSections 3.1 and 3.4 Exponential Functions (Growth and Decay)
Secions 3.1 and 3.4 Eponenial Funcions (Gowh and Decay) Chape 3. Secions 1 and 4 Page 1 of 5 Wha Would You Rahe Have... $1million, o double you money evey day fo 31 days saing wih 1cen? Day Cens Day Cens
More informationThe sudden release of a large amount of energy E into a background fluid of density
10 Poin explosion The sudden elease of a lage amoun of enegy E ino a backgound fluid of densiy ceaes a song explosion, chaaceized by a song shock wave (a blas wave ) emanaing fom he poin whee he enegy
More informationGeneral Non-Arbitrage Model. I. Partial Differential Equation for Pricing A. Traded Underlying Security
1 Geneal Non-Abiage Model I. Paial Diffeenial Equaion fo Picing A. aded Undelying Secuiy 1. Dynamics of he Asse Given by: a. ds = µ (S, )d + σ (S, )dz b. he asse can be eihe a sock, o a cuency, an index,
More informationElectromagnetic Stealth with Parallel electric and magnetic Fields
DMO / ΗΛΕΚΤΡΟΜΑΓΝΗΤΙΚΗ ΑΟΡΑΤΟΤΗΤΑ ΜΕ ΠΑΡΑΛΛΗΛΑ ΗΛΕΚΤΡΙΚΑ Κ ΜΑΓΝΗΤΙΚΑ ΠΕ ΙΑ Θ.. ΡΑΠΤΗΣ lecomagneic Sealh wih Paallel elecic and magneic Fields T.. RAPTΙS ΕΚΕΦΕ «ΗΜΟΚΡΙΤΟΣ» Τ. Θ. 68, 53 ΑΓΙΑ ΠΑΡΑΣΚΕΥΗ (Αθήνα)
More informationMEEN 617 Handout #11 MODAL ANALYSIS OF MDOF Systems with VISCOUS DAMPING
MEEN 67 Handou # MODAL ANALYSIS OF MDOF Sysems wih VISCOS DAMPING ^ Symmeic Moion of a n-dof linea sysem is descibed by he second ode diffeenial equaions M+C+K=F whee () and F () ae n ows vecos of displacemens
More informationPHYS PRACTICE EXAM 2
PHYS 1800 PRACTICE EXAM Pa I Muliple Choice Quesions [ ps each] Diecions: Cicle he one alenaive ha bes complees he saemen o answes he quesion. Unless ohewise saed, assume ideal condiions (no ai esisance,
More informationElectromagnetic interaction in dipole grids and prospective high-impedance surfaces
ADIO SCIENCE, VOL.,, doi:.29/2s36, 25 Elecomagneic ineacion in dipole gids and pospecive high-impedance sufaces C.. Simovsi Depamen of Physics, S. Peesbug Insiue of Fine Mechanics and Opics, S. Peesbug,
More informationRisk tolerance and optimal portfolio choice
Risk oleance and opimal pofolio choice Maek Musiela BNP Paibas London Copoae and Invesmen Join wok wih T. Zaiphopoulou (UT usin) Invesmens and fowad uiliies Pepin 6 Backwad and fowad dynamic uiliies and
More informationElectric Potential and Gauss s Law, Configuration Energy Challenge Problem Solutions
Poblem 1: Electic Potential an Gauss s Law, Configuation Enegy Challenge Poblem Solutions Consie a vey long o, aius an chage to a unifom linea chage ensity λ a) Calculate the electic fiel eveywhee outsie
More informationChapter Finite Difference Method for Ordinary Differential Equations
Chape 8.7 Finie Diffeence Mehod fo Odinay Diffeenial Eqaions Afe eading his chape, yo shold be able o. Undesand wha he finie diffeence mehod is and how o se i o solve poblems. Wha is he finie diffeence
More informationA note on characterization related to distributional properties of random translation, contraction and dilation of generalized order statistics
PobSa Foum, Volume 6, July 213, Pages 35 41 ISSN 974-3235 PobSa Foum is an e-jounal. Fo eails please visi www.pobsa.og.in A noe on chaaceizaion elae o isibuional popeies of anom anslaion, conacion an ilaion
More informationADJOINT MONTE CARLO PHOTON TRANSPORT IN CONTINUOUS ENERGY MODE WITH DISCRETE PHOTONS FROM ANNIHILATION
ADJOINT MONT ARLO HOTON TRANSORT IN ONTINUOUS NRGY MOD WITH DISRT HOTONS FROM ANNIHILATION J. ua Hoogenboom Inefaculy Reaco Insiue Delf Univesiy of Technology Mekelweg 5 69 JB Delf The Nehelans j.e.hoogenboom@ii.uelf.nl
More informationEN221 - Fall HW # 7 Solutions
EN221 - Fall2008 - HW # 7 Soluions Pof. Vivek Shenoy 1.) Show ha he fomulae φ v ( φ + φ L)v (1) u v ( u + u L)v (2) can be pu ino he alenaive foms φ φ v v + φv na (3) u u v v + u(v n)a (4) (a) Using v
More informationComputer Propagation Analysis Tools
Compue Popagaion Analysis Tools. Compue Popagaion Analysis Tools Inoducion By now you ae pobably geing he idea ha pedicing eceived signal sengh is a eally impoan as in he design of a wieless communicaion
More informationFullwave Analysis of Thickness and Conductivity Effects in Coupled Multilayered Hybrid and Monolithic Circuits
Poceedings of he 4h WSAS In. Confeence on lecomagneics, Wieless and Opical Communicaions, Venice, Ialy, Novembe -, 6 76 Fullwave Analysis of Thickness and Conduciviy ffecs in Coupled Mulilayeed Hybid and
More informationInt. J. Computers & Electrical Engineering, vol. 30, no. 1, pp , AN OBSERVER DESIGN PROCEDURE FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS
In. J. Compues & Elecical Engineeing, vol. 3, no., pp. 6-7, 3. AN OBSERVER DESIGN PROCEDURE FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS * ** H. Tinh *, M. Aleen ** an S. Nahavani * School o Engineeing
More informationAalborg Universitet. Melting of snow on a roof Nielsen, Anker; Claesson, Johan. Publication date: 2011
Aalbog Univesie Meling of snow on a oof Nielsen, Anke; Claesson, Jan Publicaion ae: 211 Docuen Vesion Ealy vesion, also known as pe-pin Link o publicaion fo Aalbog Univesiy Ciaion fo publishe vesion (APA):
More informationChapter 2: The Derivation of Maxwell Equations and the form of the boundary value problem
Chape : The eiaion of Mawell quaions and he fom of he bounda alue poblem In moden ime, phsics, including geophsics, soles eal-wold poblems b appling fis pinciples of phsics wih a much highe capabili han
More informationCombinatorial Approach to M/M/1 Queues. Using Hypergeometric Functions
Inenaional Mahemaical Foum, Vol 8, 03, no 0, 463-47 HIKARI Ld, wwwm-hikaicom Combinaoial Appoach o M/M/ Queues Using Hypegeomeic Funcions Jagdish Saan and Kamal Nain Depamen of Saisics, Univesiy of Delhi,
More informationAuthors name Giuliano Bettini* Alberto Bicci** Title Equivalent waveguide representation for Dirac plane waves
Auhos name Giuliano Beini* Albeo Bicci** Tile Equivalen waveguide epesenaion fo Diac plane waves Absac Ideas abou he elecon as a so of a bound elecomagneic wave and/o he elecon as elecomagneic field apped
More informationarxiv:gr-qc/ v1 9 Nov 2004
Vacuum polaizaion aoun sas: nonlocal appoximaion Alejano Saz, 1 Fancisco D. Mazzielli, an Ezequiel Alvaez 3 1 School of Mahemaical Sciences, Univesiy of Noingham Depaameno e Física Juan José Giambiagi,
More informationChapter 2 Wave Motion
Lecue 4 Chape Wae Moion Plane waes 3D Diffeenial wae equaion Spheical waes Clindical waes 3-D waes: plane waes (simples 3-D waes) ll he sufaces of consan phase of disubance fom paallel planes ha ae pependicula
More informationElastic-Plastic Deformation of a Rotating Solid Disk of Exponentially Varying Thickness and Exponentially Varying Density
Poceedings of he Inenaional MuliConfeence of Enginees Compue Scieniss 6 Vol II, IMECS 6, Mach 6-8, 6, Hong Kong Elasic-Plasic Defomaion of a Roaing Solid Dis of Exponenially Vaying hicness Exponenially
More informationJerk and Hyperjerk in a Rotating Frame of Reference
Jek an Hypejek in a Rotating Fame of Refeence Amelia Caolina Spaavigna Depatment of Applie Science an Technology, Politecnico i Toino, Italy. Abstact: Jek is the eivative of acceleation with espect to
More informationMECHANICS OF MATERIALS Poisson s Ratio
Fouh diion MCHANICS OF MATRIALS Poisson s Raio Bee Johnson DeWolf Fo a slende ba subjeced o aial loading: 0 The elongaion in he -diecion is accompanied b a conacion in he ohe diecions. Assuming ha he maeial
More informationThe k-filtering Applied to Wave Electric and Magnetic Field Measurements from Cluster
The -fileing pplied o Wave lecic and Magneic Field Measuemens fom Cluse Jean-Louis PINÇON and ndes TJULIN LPC-CNRS 3 av. de la Recheche Scienifique 4507 Oléans Fance jlpincon@cns-oleans.f OUTLINS The -fileing
More informationThe Method of Images in Velocity-Dependent Systems
>1< The Mehod of Images in Velociy-Dependen Sysems Dan Censo Ben Guion Univesiy of he Negev Depamen of Elecical and Compue Engineeing Bee Sheva, Isael 8415 censo@ee.bgu.ac.il Absac This sudy invesigaes
More informationA GENERAL METHOD TO STUDY THE MOTION IN A NON-INERTIAL REFERENCE FRAME
The Inenaional onfeence on opuaional Mechanics an Viual Engineeing OME 9 9 OTOBER 9, Basov, Roania A GENERAL METHOD TO STUDY THE MOTION IN A NON-INERTIAL REFERENE FRAME Daniel onuache, Vlaii Mainusi Technical
More information15. SIMPLE MHD EQUILIBRIA
15. SIMPLE MHD EQUILIBRIA In this Section we will examine some simple examples of MHD equilibium configuations. These will all be in cylinical geomety. They fom the basis fo moe the complicate equilibium
More informationThat is, the acceleration of the electron is larger than the acceleration of the proton by the same factor the electron is lighter than the proton.
PHY 8 Test Pactice Solutions Sping Q: [] A poton an an electon attact each othe electically so, when elease fom est, they will acceleate towa each othe. Which paticle will have a lage acceleation? (Neglect
More informationChapter Three Systems of Linear Differential Equations
Chaper Three Sysems of Linear Differenial Equaions In his chaper we are going o consier sysems of firs orer orinary ifferenial equaions. These are sysems of he form x a x a x a n x n x a x a x a n x n
More informationStress Analysis of Infinite Plate with Elliptical Hole
Sess Analysis of Infinie Plae ih Ellipical Hole Mohansing R Padeshi*, D. P. K. Shaa* * ( P.G.Suden, Depaen of Mechanical Engg, NRI s Insiue of Infoaion Science & Technology, Bhopal, India) * ( Head of,
More informationEfficient experimental detection of milling stability boundary and the optimal axial immersion for helical mills
Efficien expeimenal deecion of milling sabiliy bounday and he opimal axial immesion fo helical mills Daniel BACHRATHY Depamen of Applied Mechanics, Budapes Univesiy of Technology and Economics Muegyeem
More informationPhysics 122, Fall December 2012
Physics 1, Fall 01 6 Decembe 01 Toay in Physics 1: Examples in eview By class vote: Poblem -40: offcente chage cylines Poblem 8-39: B along axis of spinning, chage isk Poblem 30-74: selfinuctance of a
More informationPressure Vessels Thin and Thick-Walled Stress Analysis
Pessue Vessels Thin and Thick-Walled Sess Analysis y James Doane, PhD, PE Conens 1.0 Couse Oveview... 3.0 Thin-Walled Pessue Vessels... 3.1 Inoducion... 3. Sesses in Cylindical Conaines... 4..1 Hoop Sess...
More informationTHE SINE INTEGRAL. x dt t
THE SINE INTEGRAL As one learns in elemenary calculus, he limi of sin(/ as vanishes is uniy. Furhermore he funcion is even and has an infinie number of zeros locaed a ±n for n1,,3 Is plo looks like his-
More information( )( )( ) ( ) + ( ) ( ) ( )
3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13
More informationAn Open cycle and Closed cycle Gas Turbine Engines. Methods to improve the performance of simple gas turbine plants
An Open cycle and losed cycle Gas ubine Engines Mehods o impove he pefomance of simple gas ubine plans I egeneaive Gas ubine ycle: he empeaue of he exhaus gases in a simple gas ubine is highe han he empeaue
More informationr P + '% 2 r v(r) End pressures P 1 (high) and P 2 (low) P 1 , which must be independent of z, so # dz dz = P 2 " P 1 = " #P L L,
Lecue 36 Pipe Flow and Low-eynolds numbe hydodynamics 36.1 eading fo Lecues 34-35: PKT Chape 12. Will y fo Monday?: new daa shee and daf fomula shee fo final exam. Ou saing poin fo hydodynamics ae wo equaions:
More informationEquilibria of a cylindrical plasma
// Miscellaneous Execises Cylinical equilibia Equilibia of a cylinical plasma Consie a infinitely long cyline of plasma with a stong axial magnetic fiel (a geat fusion evice) Plasma pessue will cause the
More informationFINITE DIFFERENCE APPROACH TO WAVE GUIDE MODES COMPUTATION
FINITE DIFFERENCE ROCH TO WVE GUIDE MODES COMUTTION Ing.lessando Fani Elecomagneic Gou Deamen of Elecical and Eleconic Engineeing Univesiy of Cagliai iazza d mi, 93 Cagliai, Ialy SUMMRY Inoducion Finie
More informationAN EVOLUTIONARY APPROACH FOR SOLVING DIFFERENTIAL EQUATIONS
AN EVOLUTIONARY APPROACH FOR SOLVING DIFFERENTIAL EQUATIONS M. KAMESWAR RAO AND K.P. RAVINDRAN Depamen of Mechanical Engineeing, Calicu Regional Engineeing College, Keala-67 6, INDIA. Absac:- We eploe
More informationReinforcement learning
Lecue 3 Reinfocemen leaning Milos Hauskech milos@cs.pi.edu 539 Senno Squae Reinfocemen leaning We wan o lean he conol policy: : X A We see examples of x (bu oupus a ae no given) Insead of a we ge a feedback
More informationRelative and Circular Motion
Relaie and Cicula Moion a) Relaie moion b) Cenipeal acceleaion Mechanics Lecue 3 Slide 1 Mechanics Lecue 3 Slide 2 Time on Video Pelecue Looks like mosly eeyone hee has iewed enie pelecue GOOD! Thank you
More informationPHYSICS 102. Intro PHYSICS-ELECTROMAGNETISM
PHYS 0 Suen Nme: Suen Numbe: FAUTY OF SIENE Viul Miem EXAMINATION PHYSIS 0 Ino PHYSIS-EETROMAGNETISM Emines: D. Yoichi Miyh INSTRUTIONS: Aemp ll 4 quesions. All quesions hve equl weighs 0 poins ech. Answes
More informationAN EFFICIENT INTEGRAL METHOD FOR THE COMPUTATION OF THE BODIES MOTION IN ELECTROMAGNETIC FIELD
AN EFFICIENT INTEGRAL METHOD FOR THE COMPUTATION OF THE BODIES MOTION IN ELECTROMAGNETIC FIELD GEORGE-MARIAN VASILESCU, MIHAI MARICARU, BOGDAN DUMITRU VĂRĂTICEANU, MARIUS AUREL COSTEA Key wods: Eddy cuen
More informationPHY 213. General Physics II Test 2.
Univesity of Kentucky Depatment of Physics an Astonomy PHY 3. Geneal Physics Test. Date: July, 6 Time: 9:-: Answe all questions. Name: Signatue: Section: Do not flip this page until you ae tol to o so.
More informationThe Fundamental Theorems of Calculus
FunamenalTheorems.nb 1 The Funamenal Theorems of Calculus You have now been inrouce o he wo main branches of calculus: ifferenial calculus (which we inrouce wih he angen line problem) an inegral calculus
More informationAST1100 Lecture Notes
AST00 Lecue Noes 5 6: Geneal Relaiviy Basic pinciples Schwazschild geomey The geneal heoy of elaiviy may be summaized in one equaion, he Einsein equaion G µν 8πT µν, whee G µν is he Einsein enso and T
More informationPrerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART A PHYSICS
Pena Towe, oad No, Conacos Aea, isupu, Jamshedpu 83, Tel (657)89, www.penaclasses.com AIEEE PAT A PHYSICS Physics. Two elecic bulbs maked 5 W V and W V ae conneced in seies o a 44 V supply. () W () 5 W
More informationworks must be obtained from the IEEE.
NAOSTE: Nagasaki Univesiy's Ac Tile Auho(s) Opeaion chaaceisics impoveme hal-wave eciie sel exciaion Hiayama, Taashi; Higuchi, Tsuyosh Ciaion CEMS 7, pp.8-8 ssue Dae 7- URL Righ hp://hl.hanle.ne/69/6 (c)7
More informationSignals and Systems Profs. Byron Yu and Pulkit Grover Fall Midterm 1 Solutions
8-90 Signals and Sysems Profs. Byron Yu and Pulki Grover Fall 07 Miderm Soluions Name: Andrew ID: Problem Score Max 0 8 4 6 5 0 6 0 7 8 9 0 6 Toal 00 Miderm Soluions. (0 poins) Deermine wheher he following
More informationChapter 2. First Order Scalar Equations
Chaper. Firs Order Scalar Equaions We sar our sudy of differenial equaions in he same way he pioneers in his field did. We show paricular echniques o solve paricular ypes of firs order differenial equaions.
More informationSpecial Subject SC434L Digital Video Coding and Compression. ASSIGNMENT 1-Solutions Due Date: Friday 30 August 2002
SC434L DVCC Assignmen Special Sujec SC434L Digial Vieo Coing an Compession ASSINMENT -Soluions Due Dae: Fiay 30 Augus 2002 This assignmen consiss of wo pages incluing wo compulsoy quesions woh of 0% of
More informationThe shortest path between two truths in the real domain passes through the complex domain. J. Hadamard
Complex Analysis R.G. Halbud R.Halbud@ucl.ac.uk Depamen of Mahemaics Univesiy College London 202 The shoes pah beween wo uhs in he eal domain passes hough he complex domain. J. Hadamad Chape The fis fundamenal
More informationDamage Assessment in Composites using Fiber Bragg Grating Sensors. Mohanraj Prabhugoud
ABSTRACT PRABHUGOUD MOHANRAJ. Damage Assessmen in Composies using Fibe Bagg Gaing Sensos. (Unde he diecion of Assisan Pofesso Kaa J. Pees). This disseaion develops a mehodology o assess damage in composies
More informationψ(t) = V x (0)V x (t)
.93 Home Work Se No. (Professor Sow-Hsin Chen Spring Term 5. Due March 7, 5. This problem concerns calculaions of analyical expressions for he self-inermediae scaering funcion (ISF of he es paricle in
More informationb) The array factor of a N-element uniform array can be written
to Eam in Antenna Theo Time: 18 Mach 010, at 8.00 13.00. Location: Polacksbacken, Skivsal You ma bing: Laboato epots, pocket calculato, English ictiona, Råe- Westegen: Beta, Noling-Östeman: Phsics Hanbook,
More informationServomechanism Design
Sevomechanism Design Sevomechanism (sevo-sysem) is a conol sysem in which he efeence () (age, Se poin) changes as ime passes. Design mehods PID Conol u () Ke P () + K I ed () + KDe () Sae Feedback u()
More informationHeat Conduction Problem in a Thick Circular Plate and its Thermal Stresses due to Ramp Type Heating
ISSN(Online): 319-8753 ISSN (Pin): 347-671 Inenaional Jounal of Innovaive Reseac in Science, Engineeing and Tecnology (An ISO 397: 7 Ceified Oganiaion) Vol 4, Issue 1, Decembe 15 Hea Concion Poblem in
More informationOn Control Problem Described by Infinite System of First-Order Differential Equations
Ausalian Jounal of Basic and Applied Sciences 5(): 736-74 ISS 99-878 On Conol Poblem Descibed by Infinie Sysem of Fis-Ode Diffeenial Equaions Gafujan Ibagimov and Abbas Badaaya J'afau Insiue fo Mahemaical
More informationSPH4UI 28/02/2011. Total energy = K + U is constant! Electric Potential Mr. Burns. GMm
8//11 Electicity has Enegy SPH4I Electic Potential M. Buns To sepaate negative an positive chages fom each othe, wok must be one against the foce of attaction. Theefoe sepeate chages ae in a higheenegy
More informationTHERMAL PHYSICS. E nc T. W PdV. degrees of freedom. 32 m N V. P mv. Q c. AeT (emitted energy rate) E Ae T Tsurroundings. Q nc p
HRMA PHYSICS PHY 8 Final es: Compehensie Concep and Fomula Shee NB: Do no add anyhing o he fomula shee excep in he space specially assigned. hemodynamic Paamees: Volume V of mass m wih densiy ρ: V m empeaue
More informationMATH 31B: MIDTERM 2 REVIEW. x 2 e x2 2x dx = 1. ue u du 2. x 2 e x2 e x2] + C 2. dx = x ln(x) 2 2. ln x dx = x ln x x + C. 2, or dx = 2u du.
MATH 3B: MIDTERM REVIEW JOE HUGHES. Inegraion by Pars. Evaluae 3 e. Soluion: Firs make he subsiuion u =. Then =, hence 3 e = e = ue u Now inegrae by pars o ge ue u = ue u e u + C and subsiue he definiion
More informationINDEX. Transient analysis 1 Initial Conditions 1
INDEX Secion Page Transien analysis 1 Iniial Condiions 1 Please inform me of your opinion of he relaive emphasis of he review maerial by simply making commens on his page and sending i o me a: Frank Mera
More informationWORK POWER AND ENERGY Consevaive foce a) A foce is said o be consevaive if he wok done by i is independen of pah followed by he body b) Wok done by a consevaive foce fo a closed pah is zeo c) Wok done
More informationElectric Potential. Outline. Potential Energy per Unit Charge. Potential Difference. Potential Energy Difference. Quiz Thursday on Chapters 23, 24.
lectic otential Quiz Thusay on Chaptes 3, 4. Outline otential as enegy pe unit chage. Thi fom of Coulomb s Law. elations between fiel an potential. otential negy pe Unit Chage Just as the fiel is efine
More informationSection 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
Secion 3.5 Nonhomogeneous Equaions; Mehod of Undeermined Coefficiens Key Terms/Ideas: Linear Differenial operaor Nonlinear operaor Second order homogeneous DE Second order nonhomogeneous DE Soluion o homogeneous
More informationHomework 2 Solutions
Mah 308 Differenial Equaions Fall 2002 & 2. See he las page. Hoework 2 Soluions 3a). Newon s secon law of oion says ha a = F, an we know a =, so we have = F. One par of he force is graviy, g. However,
More information